Question

a light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 761 hours. a random sample of 24 light bulbs has a mean life of 733 hours. assume the population is normally distributed and the population standard deviation is 62 hours. at \\( \alpha = 0.02 \\), do you have enough evidence to reject the manufacturers claim? complete parts (a) through (e)
(b) identify the critical value(s). use technology
\\( z _ { 0 } = - 2.05 \\)
(use a comma to separate answers as needed. round to two decimal places as needed.)
identify the rejection region(s). choose the correct answer below.
(c) identify the standardized test statistic. use technology.
\\( z = - 2.21 \\) (round to two decimal places as needed.)
(d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Explanation:

Step1: Recall the decision rule for hypothesis testing

If the standardized test statistic \(z\) is less than the critical value \(z_0\), we reject the null hypothesis.

Step2: Compare \(z\) and \(z_0\)

We have \(z=- 2.21\) and \(z_0=-2.05\). Since \(-2.21<-2.05\) (i.e., \(z < z_0\)).

Answer:

A. Reject \(H_0\). There is sufficient evidence to reject the claim that mean bulb life is at least 761 hours.